Connoisseurs study not only gem quality but also proportions. The emerald image above has been manipulated to show a square emerald in the middle, an 8 x 10 on the left and an 8 x 9 millimeter emerald to the right.

Much has been written about the ‘Golden Ratio’, a ubiquitous mathematical ratio (1 : 1.618033…) which is found in an astonishing number of places – mollusk shells, sunflower florets, crystals, leaf placement patterns in plants, and even the shape of the galaxies. Notables such as Leonardo da Vinci, Kepler, Dali, Debussy and Le Corbusier have participated in its study and expressed it in their respective arts. In the image below, you can see an image of an emerald manipulated to conform exactly to this ratio.
In the 12th century, Leonardo Fibonacci discovered a simple numerical series that is the foundation for an incredible mathematical relationship behind phi. Starting with 0 and 1, each new number in the series is simply the sum of the two numbers before it. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . The ratio of each successive pair of numbers in the series approximates phi (1.618. . .) , as 5 divided by 3 is 1.666..., and 8 divided by 5 is 1.60. The ratios of the successive numbers in the Fibonacci series quickly converge on Phi. After the 40th number in the series, the ratio is accurate to 15 decimal places(1.618033988749895).

As you can see, a gem cut to the proportions of the Golden Ratio seems too long. Or do they? It is a subjective call; you might like long stones. However, when golden ratio emeralds are oriented vertically, as for earrings on the right, it seems that it would be quite lovely (at least to me). The beauty of emeralds from Colombia is that they are cut for maximum retention of weight from the rough. Each is a unique piece; like the work of art that it is. That is why you will see length to width ratios from 1:1 to 1:1.4 all the way up to 1:1.618. Placement of diamonds and gold can add or subtract from the length to complete a jewelry piece: turning it into not flat art but sculpture.